Welcome to the Q&A Forum

You may have already tried this (https://megalytic.com/blog/how-to-filter-out-fake-referrals-and-other-google-analytics-spam) as I believe it is one of the more common articles, but it suggests setting up a filter to use hostnames and testing it with a segment. This has worked well for us. You have to be careful and make sure you use ALL the relevant hostnames and that your expression doesn't contain errors.

Matt Cutts from Google addressed this in a short Youtube video you can watch here. I hope that helps!

It sounds like you may already know this, but other people reading this post for advice may not.  Don't forget to make sure Google didn't take any manual actions against the website when it was compromised. You can do by checking Google WMT under "Search Traffic" -> "Manual Actions". If Google did impose a manual action you will need to submit a reconsideration request to Google. These requests can take 2-3 weeks to process. I hope that helps!

If you are wanting to target multiple keywords then it obviously makes sense to utilize some of your other website pages to rank for those keywords. If one of your other pages answers questions or provides information on a specific topic then I would try to get relevant blogs other websites to link back to that specific page. For example, if your page discusses the benefits of animal adoption, then it would be beneficial if the local Humane Society linked to it.

If you do the appropriate amount of keyword and other research before making the changes, then you most likely wont be super surprised by the way Google interprets your changes.

As an additional safe guard you should closely monitor your rankings after you make the changes. If you notice too much of negative impact as a result of the changes, change your content back and start over with a different approach. Research and monitoring are key!